DESIGN OF MODIFIED MICROWAVE POWER DIVIDER FOR RADAR
ELECTRONIC WARFARE TRANSCEIVING SYSTEM
AMIR RUDIN BIN MAT DIN
A project report submitted in partial fulfillment of the requirement for the award of
the degree of Master of Engineering (Electrical-Electronic and Telecommunication)
Faculty of Electrical Engineering
Universiti Teknologi Malaysia
APRIL 2007
iii
Special dedicated to my beloved parents and friends
for their support and encouragement.
iv
ACKNOWLEDGEMENT
First and foremost, I would like to take this opportunity to thank all the
important people who were responsible in making this project a success, may it be
directly or indirectly involved. Thank you for making this thesis a reality.
My special appreciation to my supervisor, Associate Professor Dr Mazlina
Esa who had coached and guided me in every possible way to ensure this project is a
success. My special thanks to all my course mates.
I would also like to thank my Commanding Officers, Chief of EW Wing for
their support and assistance in making this project a success. Last but not least,
special thank to the Chief of Signals Officer for giving me the support and
opportunity to future my studies.
v
ABSTRACT
Radar electronic warfare beam forming transceiving system requires robust
components in order to fully utilize the radar functionality. One such essential
component is the power divider and its complementary power combining circuitry.
Conventional power divider operates at a fundamental frequency and odd harmonics.
The thesis presents the design of a broadband modified 2-way microwave power
divider with the capability of delivering an identical signal as the backup to a radar
electronic warfare transceiving system. The chosen band of the radar system is from
0.7 GHz to 3 GHz. The design starts with the basic conventional 2-way Wilkinson
power divider. Modifications were done in the form of having trisection transmission
lines and integrate it with either single or combination of lumped element loads of
resistor, capacitor and inductor. The component values were initially computed.
Investigations on the configurations were performed using an electromagnetic
simulation software. It can be concluded that an optimum broadband modified power
divider has been successfully designed to operate between 0.7 GHz to 3 GHz with
equal power division of -3 dB at each output port.
vi
ABSTRAK
Sistem pemancar-penerima radar peperangan elektronik membentuk alur
memerlukan komponen tahan lasak bagi memenuhi keperluan operasi radar. Satu
komponen asas penting ialah litar pembahagi dan penggabung kuasa. Pembahagi
kuasa lazim beroperasi pada frekuensi asas dan harmonik ganjil. Tesis ini
membentangkan rekabentuk pembahagi kuasa gelombang mikro jalurluas dengan
keupayaan menghasilkan isyarat serbasama sebagai isyarat kedua bagi sistem
pemancar-penerima radar peperangan elektronik. Jalur operasi sistem radar ini
dipilih bagi julat 0.7 GHz sehingga 3 GHz. Penyelidikan ke atas Rekabentuk litar
dimulai dengan litar asas pembahagi kuasa 2-hala. Seterusnya, ubahsuaian dibuat
terhadap litar dalam bentuk talian penghantaran tiga bahagian. Ini kemudiannya
diintegrasi dengan beban tergumpal perintang, kapasitor dan induktor, tunggal atau
gabungan. Nilai komponen dikira terlebih dahulu. Kajian menyeluruh terhadap
prestasi rekabentuk dibuat menggunakan perisian simulasi elektromagnet. Dapat
disimpulkan bahawa pembahagi kuasa yang optimum telah berjaya direka untuk
berkendali antara 0.7 GHz dan 3 GHz. Ia mempunyai ciri pembahagian kuasa yang
sama sebesar -3 dB pada setiap port keluaran.
vii
TABLE OF CONTENTS
TITLE
i
DECLARATION
ii
DEDICATION
iii
ACKNOWLEDGEMENT
iv
ABSTRACT
v
ABSTRAK
vi
TABLE OF CONTENTS
vii
LIST OF TABLES
ix
LIST OF FIGURES
x
LIST OF SYMBOLS
xiii
LIST OF ABBREVIATIONS
xiv
LIST OF APPENDICES
xv
CHAPTER
1
TITLE
PAGE
INTRODUCTION
1.1
Background of the Project
2
1.2
Objective of the Project
3
1.3
Problem Statement
3
1.4
Scopes of Project
4
1.5
Organization of Thesis
6
viii
2
3
FUNDAMENTALS OF POWER DIVIDERS
2.1
Introduction
7
2.2
Microstrip Technology
8
2.3
Basic Properties of Power Divider
10
2.4
Wilkinson Power Divider
13
2.4.1
Introduction
13
2.4.2
Brief Basic Theory
14
2.5
Design of Modified Wilkinson Power Divider
17
2.6
Design Methodology
22
SOFTWARE USED
3.1
4
AWR Microwave Office
RESLUTS AND DISCUSSIONS
4.1
Basic Conventional Wilkinson Power Divider
4.2
Tri Section Modified Wilkinson Power Divider with
Lumped Element
4.3
5
24
27
34
Tri Section Modified Wilkinson Power Divider with
R Segment in Cascade
45
4.4
Improving the Modified Wilkinson Power Divider
53
4.5
Summary
56
CONCLUSIONS AND RECOMMANDATIONS
5.1
Conclusion
57
5.2
Suggestions for Further Research
58
REFERENCES
59
APPENDIX
62
ix
LIST OF TABLES
TABLE NO.
TITLE
PAGE
4.1
Prototype values for conventional design.
27
4.2
Simulated data reading for conventional WPD.
33
4.3
Simulated results with varying L.
39
4.4
Simulated results with varying C.
42
4.5
Simulated results with varying L and C.
45
4.6
Performance comparisons between all WPD configurations.
56
x
LIST OF FIGURES
FIGURE NO.
TITLE
PAGE
1.1
Antenna sectors of the ELINT System.
2
1.2
Land Mobile ELINT System.
2
1.3
Conventional 2-way WPD.
5
1.4
Dual-band WPD with open stub.
5
1.5
2 Way WPD with RLC.
6
2.1
Power division.
8
2.2
Cross sectional view of a microstrip line.
8
2.3
Electric field and magnetic field line in microstrip line.
9
2.4
Power divider developed by Wilkinson.
13
2.5
Schematic diagram of a Wilkinson power divider.
14
2.6
15
2.7
Symmetrical circuit for the even-odd mode analysis of
Wilkinson network
Simplified equivalent circuit for the even mode analysis .
2.8
Simplified equivalent circuit for the odd mode analysis .
16
2.9
Simplified equivalent circuit of the Wilkinson power divider.
16
2.10
18
2.11
Wilkinson power divider based on the transmission line
transformer structure .
Layout of a Tri Section Wilkinson Power Divider.
2.12
Simulated return losses responses of a Tri Section WPD.
21
2.13
Simulated isolation responses of a Tri Section WPD.
21
2.14
Simulated coupling responses of a Tri Section WPD.
22
2.15
Design Methodology.
23
3.1
An Example of AWR Microwave Office sheet.
25
15
20
xi
4.1
Basic Conventional WPD Circuit.
28
4.2
Simulated return loss of basic WPD at 0.9 GHz.
28
4.3
Simulated isolation of basic WPD at 0.9 GHz.
29
4.4
Simulated power division of basic WPD at 0.9 GHz.
29
4.5
Simulated return loss of basic WPD at 1.8 GHz.
30
4.6
Simulated isolation of basic WPD at 1.8 GHz.
30
4.7
Simulated power division of basic WPD at 1.8 GHz.
31
4.8
Simulated return loss of basic WPD at 2.7 GHz.
31
4.9
Simulated isolation of basic WPD at 2.7 GHz.
32
4.10
Simulated power division of basic WPD at 2.7 GHz.
32
4.11
The schematic layout for basic Tri Section Modified
WPD.
Simulated return loss of basic Tri Section Modified
WPD.
Simulated isolation of basic Tri Section Modified WPD.
34
Simulated power division of basic Tri Section Modified
WPD.
The schematic layout for Tri Section Modified WPD
with RL Element.
Simulated return loss of Tri Section Modified WPD
with RL Element.
Simulated isolation of Tri Section Modified WPD with
RL Element.
Simulated coupling or power division of Tri Section
Modified WPD with RL Element.
The schematic layout for Tri Section Modified WPD
with RC Element.
Simulated return loss of Tri Section Modified WPD
with RC Element.
Simulated isolation of Tri Section Modified WPD with
RC Element.
Simulated coupling or power division of Tri Section
Modified WPD with RC Element.
The schematic layout for Tri Section Modified WPD
with RLC Element.
36
4.12
4.13
4.14
4.15
4.16
4.17
4.18
4.19
4.20
4.21
4.22
4.23
35
35
37
37
38
38
40
40
41
41
43
xii
4.24
4.25
4.26
4.27
4.28
4.29
4.30
4.31
4.32
4.33
4.34
4.35
4.36
4.37
4.38
4.39
4.40
4.41
4.42
Simulated return loss of Tri Section Modified WPD
with RLC Element.
Simulated isolation of Tri Section Modified WPD with
RLC Element.
Simulated coupling or power division of Tri Section
Modified WPD with RLC Element.
The schematic layout for Tri Section Modified WPD
with 2nd Segment in Cascade.
Simulated return loss of Tri Section Modified WPD
with 2nd Segment in Cascade.
Simulated isolation of Tri Section Modified WPD with
2nd Segment in Cascade.
Simulated power division of Tri Section Modified WPD
with 2nd Segment in Cascade.
The schematic layout for Tri Section Modified WPD
with 1st Segment in Cascade.
Simulated return loss of Tri Section Modified WPD
with 1st Segment in Cascade.
Simulated isolation of Tri Section Modified WPD with
1st Segment in Cascade.
Simulated power division of Tri Section Modified WPD
with 1st Segment in Cascade.
The schematic layout for Tri Section Modified WPD
with Full Segment in Cascade.
Simulated return loss of Tri Section Modified WPD
with Full Segment in Cascade.
Simulated isolation of Tri Section Modified WPD with
Full Segment in Cascade.
Simulated power division of Tri Section Modified WPD
with Full Segment in Cascade.
The schematic layout for Final Design of Tri Section
Modified WPD with Full Segment in Cascade.
Simulated return loss for Final Design of Tri Section
Modified WPD with Full Segment in Cascade.
Simulated isolation for Final Design of Tri Section
Modified WPD with Full Segment in Cascade.
Simulated power division for Final Design of Tri
Section Modified WPD with Full Segment in Cascade.
43
44
44
46
46
47
47
48
49
49
50
51
51
52
52
54
54
55
55
xiii
LIST OF SYMBOLS
h
-
Thickness of Substrate

r
-
Relative Permittivity
ε
e
-
Effective Permittivity
vp
-
Phase Velocity
α
-
Attenuation Constant
β
-
Phase Constant
t
-
Thickness of Conductor
R
-
Resistance
G
-
Conductance
L
-
Inductance
C
-
Capacitance
Z0
-
Characteristic Impedance
ZL
-
Load Impedance
Γ
-
Reflection Coefficient
xiv
LIST OF ABBREVIATIONS
EW
Electronic Warfare
ELINT
Electronic Intelligence
WPD
Wilkinson Power Divider
MWO
Microwave Office
EM
Electromagnetic
BW
Bandwidth
xv
LIST OF APPENDICES
APPENDIX
A
TITLE
Simulation Result for Tri Section Modified WPD
PAGE
62
1
CHAPTER I
INTRODUCTION
1.1
Background of the Project
Power combiners and dividers are passive devices. These are needed in
microwave systems for combining power of signals from several inputs and
distributing the power of an input signal into several outputs, respectively. The
combination can be at the front end, whereby it may be too laborious to design a high
power amplifier. Instead, each output of the power divider can then be amplified, and
all the amplified signals were then recombined. This will result in a highly amplified
signal, with the amplification done using low power amplifiers.
One radar system being studied in this project is the Electronic Intelligence
System or ELINT station [1]. It is a passive radar, functioning as a noncommunication system. Its current operating capability is from 0.7 GHz to 18 GHz,
with four antenna sectors, as illustrated in Figure 1.1. The bandwidth of the sectors is
0.7 GHz to 3 GHz, 3 GHz to 8 GHz and 8 GHz to 18 GHz, respectively. The 4th
sector is a dummy and can be upgraded.
The power divider is proposed to provide a back-up for the incoming signals.
The station is part of an electronic warfare system available. A 2-way microwave
power divider will ensures two identical signals of half the input signal be delivered
2
from the inception to the receiving circuitry. One signal will remain in operation. The
second identical signal serves as the backup to the ELINT system. Wilkinson Power
Divider (WPD) has been identified as the suitable configuration due to its simple
circuitry. It also has excellent characteristics of excellent impedance matched at all
ports, lossless, good isolation, compact, and can easily be fabricated using cost
effective readily available materials. The narrowband property can be improved for
broadband characteristics. The land mobile ELINT system is shown in Figure 1.2.
Figure 1.1
Antenna sectors of the ELINT System [1].
Figure 1.2
Land Mobile ELINT System [1].
3
1.2
Objective of the Project
The objective of this project is to design a modified power divider with the
capability of delivering an identical signal as the backup to a radar electronic warfare
transceiving system. It has to exhibit broadband characteristic within 0.7 GHz to 3
GHz. The bandwidth was chosen as it is the smallest range available.
1.3
Problem Statement
In recent years, the microwave technology has undergone tremendous
development. One of such development is the Radar and Electronic Intelligence
system known as the ELINT system. The ELINT system is a very expensive set-up in
electronic warfare area. It is also a complex system. However, there is a limitation
with regards to measurement and sampling aspects, due to the quality of the receiving
signal. There is a crucial need for a backup system in the usage to enhance its
capabilities. Hence, the proposed backup system in the form of a robust broadband
microwave power divider can be used for monitoring and surveillance purposes.
Accurate data can then be determined based on the quality of the pickup or received
signal. The quality of the receiving signal can be significantly improved.
4
1.4
Scopes of Project
The scopes of the project are as follows:
(i)
design of single basic WPDs, each operating at 0.9 GHz, 1.8 GHz and
2.7 GHz. These single frequencies will form the three initial main
operating frequencies in the desired broadband region. Simulate [2]
and investigate the possibility of improving the circuit characteristics.
Simulations were done using electromagnetic simulation software,
AWR Microwave Office 2004.
(ii)
modification of the conventional WPD configuration into tri-sections
of transmission lines to reflect the three identified main operating
frequencies. Simulations are performed and the performances
investigated.
(iii)
further modifications using lumped element loadings.
(iv)
fine-tune
for
optimum
configuration
which
fulfill
desired
specifications.
The desired design specifications are as follows:
(i)
broadband operating frequencies
: 0.7 GHz to 3 GHz
(ii)
3 dB coupling or half-power division
: between ports 1 and 2,
and ports 1 and 3
(iii)
good isolation of < -10 dB
: between ports 2 and 3
(iv)
good return loss of < -10 dB
: at ports 1, 2 and 3
The chosen microwave board has the following parameters:
(i)
PTFE microwave board
: RO4003 (Rogers)
(ii)
thickness of substrate , h
: 0.81 mm
(iii)
relative permittivity of substrate, 
r
: 3.38
(iv)
loss tangent of substrate, tan 
: 0.0027
(v)
thickness of conductor, t
: 35 µm
5
The basic single operation conventional WPD is shown in Figure 1.2 [3]. Two
configurations available in the literature are used as the main references for this
project [4], [5]. The corresponding circuits are shown in Figures 1.3 and 1.4,
respectively.
Figure 1.3
Figure 1.4
Conventional 2-way WPD [3].
Dual-band WPD with open stub [4].
6
Figure 1.5
1.5
2 Way WPD with RLC [5].
Organization of Thesis
This thesis consists of five chapters. Chapter I present the objectives of the
project, the problem statement, project background, the scope of project, and lastly
the organization of this thesis.
Chapter II discusses the Power Divider theory, discussion include scattering
parameter, odd and even analysis for Wilkinson Power Divider and its response,
characteristic and design methodology.
Chapter III discusses on the software used in the design, mainly AWR
Microwave Office 2004.
Chapter IV presents the results and discussions were made.
Chapter V concludes the thesis and suggestions for future work were made.
7
CHAPTER II
FUNDAMENTALS OF POWER DIVIDERS
2.1
Introduction
Power dividers are passive microwave components. They are used either for
power division or power combining. In a power division circuitry, an input signal is
divided by the circuit into two or more signals of lesser equal or unequal powers.
This is illustrated in Figure 2.1 for a three-port circuit. There several forms of power
dividing networks such as the T junction, directional coupler and hybrid coupler.
Power dividers often are of the equal power division (or -3 dB) type, but unequal
power division ratios are also possible. This project focuses on the Wilkinson power
divider, made of microstrip transmission line sections and shunt components.
P1
Power
divider
P2 = αP1
P3 = (1 - α) P1
Figure 2.1 Power division [3].
P1, input power at port 1
P2, output power at port 2
P3, output power at port 3
α, power division factor
8
2.2
Microstrip Technology
Microstrip line is a type of transmission line commonly used to design
power dividers. It is simple to be manufactured with photolithography technology.
In addition, it eases the integration with other passive and active microwave
components. A microstrip line consists of dielectric substrate layer with specific
relative permittivity (ε
r ) and thickness of h, conductor track of width w on top of the
substrate, and ground layer underneath the substrate. The configuration is shown in
Figure 2.2. Both conductor layers have the same thicknesses of t (or T, as in the
figure). The track length has the dimension l.
Figure 2.2
Cross sectional view of a microstrip line [6].
Since each conductor layer lies between two different dielectric zones, i.e. e
dielectric substrate and air, the electric field lines of the microstrip exist within the
dielectric substrate and partly in the air zone above the conductor layer. The electric
and magnetic field lines are shown in Figure 2.3. Hence, the term effective
permittivity (ε
e) is introduced and taken into account in the analysis of microstrip
lines and devices. ε
e can be assumed as a homogeneous medium substituting air and
dielectric substrate zones. The value of ε
e is greater than air permittivity (= 1) but
less than ε
r.
9
Figure 2.3
Electric field and magnetic field line in microstrip line [7].
Therefore, the parameters phase velocity (vp) and phase constant (β) of the
wave travelling through the microstrip line are derived based on ε
e as follows [7]:
Vp 
c
e
(2.1)
k 0 
e
(2.2)
where c and k0 are the propagating wave velocity in free space and wave number,
respectively. The ε
e can be determined using the formulation [7]:
1 r 1
e  r

2
2
1
(2.3)
12h
1
w
The characteristic impedance of the line is then given by [7]:
 60 8h w 
ln   


 e w 4h 

Z 0 
120

 w

w 1.444 


 e h 1.393 0.667 ln 
h


 
for
w
1
h
for
w
1
h
(2.4)
10
If the line impedance is known, the ratio of w and h is given by [7]:
0. 11
 Z0 r 1 r 1

0.23 


 8e 60 2 r 1 r 
w
for 2
 Z 1 1 0.11
0
r
r
h
 
0.23 

2

60 2 
1


r

r 



e

2

w 

h 


 377 

1
377 
0.61
w


2 3771ln
 for 2
2
1
r 
ln
1
0.39 





2Z0 
2Z0 

h

r
r
r 
r
r 
2Z0 
 2







2.3
(2.5)
Basic Properties of Power Divider
The simplest power divider circuit has three ports. The behaviour of the
circuit can be explaines using the scattering parameters. The scattering matrix of is
composed of nine components given by [3]:

S11 S12 S13 


S 
S21 S22 S 23 



S
S
S
31
32
33 
The properties of a power divider are described as follows [3]:
(2.6)
11
(a)
Matching property
All ports need to be impedance matched so that minimum reflection
occurred at each port. For a network to be well-matched, it should have reflection
coefficients Sij = 0 for i = j. That means the value of the diagonal components equal
to zero, or the matrix rewritten as:
0 S12 S13 

S 
S21 0 S23 




S
S
0
31
32

(b)
(2.7)
Reciprocal property
A reciprocal network means that the transmission between any two ports
suffers similar power losses despite having different propagation directions. A
network is reciprocal if it is a passive network and consists of isotropic materials,
with uniform electrical properties. The property is indicated by Sij = Sji, which
means that the scattering matrix components are symmetrical across the diagonal
from up left to the bottom right. Hence, the matrix can be written as:
S11 S12 S13 



S 
S12 S22 S23 



S
S
S
13
23
33 
(2.8)
12
(c)
Lossless property
An ideal passive network is said to be lossless, i.e, no energy is converted to
heat or radiated along the path of wave propagation. This differs from an active
network. In a lossless network, incident energy at one port equals the sum of total
energy leaving other ports. Reflected energy occurred at the incident port, and no
energy is converted into other form. From the scattering matrix, when a matched
network is completely lossless, the following conditions must be satisfied:
S *12S13 0
(2.9)
S *21S 23 0
(2.10)
S *31S 32 0
(2.11)
2
2
S12 S13 1
2
S 21 S 23
2
S 31 S 32
2
2
1
1
(2.12)
(2.13)
(2.14)
For an ideal case, the sum of square of each component in a row equals
unity. In reality, that sum never achieve 1 but is usually less than 1. This indicates
that the energy is somehow converted into other forms. In general, it is quite
difficult or almost impossible to achieve an ideal lossless network. Moreover, ideal
conditions would make Sij ≠Sji , which means the network is nonreciprocal. It can
be concluded that a matched reciprocal lossless network is unachievable with a
simple power divider.
13
2.4
Wilkinson Power Divider
2.4.1
Introduction
Wilkinson power divider was proposed by E. J. Wilkinson [6], as a method
of distributing power to attain equiphase and equiamplitude condition. The design,
is depicted in Figure 2.4. It was based on a coaxial line as the input. The hollow
inner conductor is split into 8 splines of λ/4 long each, and linked by a shorting
plate. At the back end of spline, an internal resistor is placed to connect them
radially to a common junction. Finally, the output connectors are attached at the end
of each spline. It was noted that all splines were designed to be at the same potential
when signal is supplied to the input coaxial line and matched loads are connected to
the outputs. This idea is indeed amazing because a power divider which is lossless,
reciprocal, and having matched ports has been proposed. Such properties were
never achievable using a T-junction power divider.
Figure 2.4
Power divider developed by Wilkinson [8].
14
2.4.2
Brief Basic Theory
It has been discussed in Section 2.3 that a simple power divider cannot
simultaneously have all the properties of lossless, reciprocal, and matched. Hence,
the Wilkinson power divider was developed. Here, an isolation resistor is placed
between the output ports to help achieve the properties. Dissipation of energy
occurs only in isolation resistor when signal enters the network from any output
port. However, it should not affect Wilkinson network efficiency. Besides, this
isolation resistor provides perfect isolation to protect output ports at the operating
frequency. Generally, Wilkinson power divider can have any number of output
ports. A basic three port Wilkinson power divider of port characteristic impedance
Z0 is schematically shown in Figure 2.5.
Figure 2.5
Schematic diagram of a Wilkinson power divider [6].
To analyze the Wilkinson network, two approaches are used; the even-mode
analysis and the odd-mode analysis [3]. The symmetrical circuit is illustrated in
Figure 2.6 [ref?]. The circuit can be simplified for each mode, as shown in Figures
2.7 and 2.8. Figure 2.9 shows the simplified equivalent circuit of the power divider.
15
Figure 2.6
Figure 2.7
Symmetrical circuit for the even-odd mode analysis of
Wilkinson network [3].
Simplified equivalent circuit for the even mode analysis [3].
16
Figure 2.8
Figure 2.9
Simplified equivalent circuit for the odd mode analysis [3].
Simplified equivalent circuit of the Wilkinson power divider [3].
For an excellent impedance match at the input, S11 at port 1 = 0. The
transmission from port 1 to port 2 (or S21) as well as from port 2 to port 1 (S12) is
defined as:
17
j
S 21 S12 
2
(2.15)
-j/√2 in dB unit is –3 dB. Due to the symmetrical nature of the circuit, S31 and S13
should also equal to –3 dB. Since port 2 and port 3 are matched for both even and
odd modes, the reflections at both ports (S22 and S33) are zero. Isolations between
ports 2 and 3 (S23 or S 32) should also be zero, considering open circuit for even
mode and short circuit for odd mode.
2.5
Design of Modified Wilkinson Power Divider
Multistandard operation of wireless transceivers is of increasing importance
in practical applications. Hence, components that work at broadband frequencies are
of interest. In this thesis, the proposed design uses an equal-split Wilkinson power
divider which can be designed to be matched and have good isolation at three
selected arbitrary frequencies by employing the three-section transformer. The
circuit was first analyzed in order to develop a synthesis procedure. The technique
was then demonstrated through simulations within the 0.7 GHz to 2.4 GHz range.
The conventional Wilkinson divider, with terminating impedances of Z0, can
be reduced to a /4 transformer as illustrated in Figure 2.10(a). The bisection of the
circuit for even and odd-mode excitations is shown. The even-odd mode analysis
can be applied as the conventional circuit is symmetrical across the midplane
(shown as dashed line). It can be seen that the basic cell of the Wilkinson circuit is a
/4 transmission line transformer, which transforms the impedance 2Z0 to Z0. In
Figure 2.10(b), the concept is applied to a three-section transmission line
transformer as the equal-split Wilkinson divider. Three resistors were used to
achieve good isolation performance. The three sections Wilkinson retains symmetry
18
across the midplane. The three section transmission line transformer is comprised of
three transmission line sections of characteristic impedances Z1, Z2 and Z3.
(a)
(b)
Figure 2.10
Wilkinson power divider based on the transmission line transformer
structure [9].
By considering the circuit in an even-mode excitation, the three section
transmission line transformer must match the impedance 2Z0 to Z0 at f1, f2 and f3,
and simultaneously. With this condition, the design parameters of the three sections
transmission line transformer can be derived.
Using
f
u1  2
f1
and
f
u2  3
f1
(2.16, 2.17)
19
It was found that [9]
1 .361
e 0.451u1
Z1 [3 .595u 12 11.686u1 59.52 ]
e
u2
10 .051e1. 09u1
(2.18)
Knowing Z1 the parameters of the three section transmission line
transformer can be derived from the following as:
Z 2  2 Z0
Z 22
Z3 
and
Z1
(2.19, 2.20)
The synthesis of the broadband equal split Wilkinson power divider starts by
determining the frequency ratios and from the three required frequencies of
operation. Using equations (2.16) to (2.17), all the parameters of the proposed
Wilkinson circuit are then derived. Finally, the physical parameters of the circuit
depending on the transmission media are synthesized from the electrical parameters
obtained.
For impedance matching to Z0 at port 2, where ω0 = 2πf0, two equations for
two unknown of L and C are obtained [5];
(1 .772Z0 )
L
0 Z0
(2.21)
0. 28
C
0 Z 0
(2.22)
An example of designing a Tri Section Wilkinson Power Divider at f0 , 2f0
and 3fo, where f0 = 1 GHz, is shown next.
20
Figure 2.11
Layout of a Tri Section Wilkinson Power Divider.
By using equations (2.16) to (2.22),
u1 = 2GHz/1GHz = 2
u2 = 3GHz/1GHz = 3
1 .361
e 0.451u1
Z1 [3 .595u 12 11.686u1 59.52 ]
or,
Z1
3.595(2)
=
2
e
u2

10 .051e1. 09u1
11.686( 2) 59.52 e 3 (1.361e
Therefore, Z2 = √2 x 50 = 70.711 Ω
and
0. 451u
) /(10. 051e1 .09u )

= 58.8 Ω
Z3 = 70.7112/50.55 = 85.00 Ω
Then, set R to be equal 2Z0 i.e. 2Z0 = 2 x 50 = 100 Ω. The L and C vaues are
L = 1.77 (Z0/ω0) = 1.77 ( 50/ω0) = 14 nH, and
C = 0.28 / (Z0/ω0) = 0.28 / (50/ω0) = 0.9 pF
Examples of the simulated results are shown in Figures 2.12 to 2.14.
21
Figure 2.12
Figure 2.13
Simulated return losses responses of a Tri Section WPD.
Simulated isolation responses of a Tri Section WPD.
22
Figure 2.14
Simulated coupling responses of a Tri Section WPD.
From Figure 2.12, the excellent broadband return losses over 2.3 GHz range
is observed. The output ports are equally better matched with the optimums at 1.5
GHz. In Figure 2.13, an excellent isolation between output ports from 0.7 GHz to
2.5 GHz are shown. An equal power division of -3 dB at the output ports over 3
GHz range can be observed in Figure 2.14.
2.6
Design Methodology
The design starts the single basic WPD that operates at 0.9 GHz, 1.8 GHz
and 2.7 GHz. These were simulated and analysed for the possibility of improving
the circuit characteristics. The conventional WPD configuration is then modified for
achieving broadband characteristic. Simulations were carried out with AWR
Microwave Office 2004. The performances of the design modified WPD were
analyzed and the optimum design structure is determined. Comparisons with the
basic configuration was made. The overall flow of the design is shown in Figure
2.15.
23
Start
Study the WPD fundamental and theory.
Investigate possibility of improving the
characteristic of WPD.
Modify the conventional WPD
configuration for broadband
Simulate the conventional and modified
WPD configuration with AWR
Microwave Office
Analyze simulation result:
broadband, isolation & loss
Result Agree?
‘no’
‘yes’
Obtain equivalent circuit for the modified
configuration
Simplify the equivalent circuit
End
Figure 2.15
Design Methodology.
24
CHAPTER III
SOFTWARE USED
AWR Microwave Office 2004 software was used for all the simulation
work. This chapter briefly explained the usage.
3.1
AWR Microwave Office
The AWR Design Environment comprises two powerful tools that can be
used together to create an integrated system and RF design environment: Visual
System Simulator (VSS) and Microwave Office (MWO). The tool used in the
simulation work is the MWO. It has many functions and main tools.
Microwave Office enables the design of circuits either in schematics or its
layout configuration. It can perform simulations using several simulation engines
and display the output in a wide variety of graphical forms. It can also tune or
optimize the designs. The changes are automatic and immediately reflected in the
layout. Figure 3.1 shows an example of the MWO sheet.
25
Figure 3.1
An Example of AWR Microwave Office sheet.
Several tools used in the simulation are as follows:
(i)
Working with Schematics and Netlists in MWO
A schematic is a graphical representation of a circuit while a netlist is
a text-based description. An MWO project can include multiple linear and
nonlinear schematics and netlists.
(ii)
Using the Element Browser
The Element Browser gives the user access to a comprehensive
database of hierarchical groups of circuit elements for schematics and
system blocks for system diagrams. The XML Libraries folders in the
26
Element Browser provide a wide range of electrical models and S-parameter
files from the manufacturers. Circuit elements include models, sources,
ports, probes, measurement devices, data libraries, and model libraries that
can be placed in a circuit schematic for linear and non-linear simulations.
(iii)
Using the Linear Simulator
Linear simulators use nodal analysis to simulate the characteristics of
a circuit. Linear simulations are used for circuits such as low noise
amplifiers, filters, and couplers whose elements can be characterized by an
admittance matrix. Linear simulators typically generate measurements such
as gain, stability, noise figure, reflection coefficient, noise circles, and gain
circles.
(iv)
Creating Output Graphs and Measurements
MWO can view the results of the simulated circuit and system
simulations in various graphical forms. Before performing a simulation, the
user can create a graph and specify the data, or measurements to be plotted.
Measurements can include gain, noise or scattering coefficients.
27
CHAPTER IV
RESULTS AND DISCUSSIONS
4.1
Basic Conventional Wilkinson Power Divider
The design starts with the basic conventional WPD at three single operating
frequencies (0.9 GHz, 1.8 GHz and 2.7 GHz). Each circuit has one input port and
two ports and one isolating resistor for separating ports 2 and 3. The prototype
values for the design are obtained and tabulated in Table 4.1.
Table 4.1
Parameter
Prototype values for conventional design.
Operating Frequency
0.9 GHz
1.8 GHz
2.7 GHz
Z1
70.711 Ω
70.711 Ω
70.711 Ω
Z0
50 Ω
50 Ω
50 Ω
R
100 Ω
100 Ω
100 Ω
The basic schematic circuit layout for the conventional WPD is shown in
Figure 4.1.
28
Figure 4.1
Basic Conventional WPD Circuit.
The simulation results for the basic conventional WPD with different range
of single operating frequencies are shown in Figures 4.2 to 4.10.
(i)
Operating frequency of 0.9 GHz
Figure 4.2
Simulated return loss of basic WPD at 0.9 GHz.
29
Figure 4.3
Figure 4.4
Simulated isolation of basic WPD at 0.9 GHz.
Simulated coupling or power division of basic WPD at 0.9 GHz.
30
(ii)
Operating Frequency of 1.8 GHz
Figure 4.5
Figure 4.6
Simulated return loss of basic WPD at 1.8 GHz.
Simulated isolation of basic WPD at 1.8 GHz.
31
Figure 4.7
(iii)
Simulated power division of basic WPD at 1.8 GHz.
Operating Frequency of 2.7 GHz
Figure 4.8
Simulated return loss of basic WPD at 2.7 GHz.
32
Figure 4.9
Figure 4.10
Simulated isolation of basic WPD at 2.7 GHz.
Simulated coupling or power division of basic WPD at 2.7 GHz.
33
Table 4.2
Operating
Simulated data reading for conventional WPD.
Return Loss
Isolation
Power Division
Bandwidth
0.9 GHz
-120 dB
-120 dB
-3.4 dB
0.9 GHz
1.8 GHz
-120 dB
-120 dB
-3.4 dB
1.4 GHz
2.7 GHz
-120 dB
-120 dB
-3.4 dB
1.8 GHz
Frequency
There are three single operating frequencies that have been used for the
simulation. From MWO simulation tabulated in Table 4.2, the WPD designed at 0.9
GHz exhibits excellent return losses of -120 dB at all ports and the isolation
between ports is -120 dB. Equal power division from Port 1 to Ports 2 and 3 with
very small loss of 0.4 dB observed are observed. These agree with theory.
For WPD designed at 1.8 GHz, it exhibits excellent return losses of -120 dB
at all ports and narrow -10 dB BW. It also exhibits excellent isolation of -120 dB
between ports 2 and 3. These agree with theory.
For WPD designed at 2.7 GHz, it exhibits excellent return losses of -120 dB
at all ports and narrow -10 dB BW. It also exhibits excellent isolation of -120 dB
between ports 2 and 3. These agree with theory.
It can be inferred that the circuit can be improved to achieve broadband
characteristics. The next section discusses the modifications that have been done by
introducing the tri section modified WPD circuit.
34
4.2
Tri Section Modified Wilkinson Power Divider with Lumped Element
The configuration of this circuit uses three sections of quarter-wave
transformer by using three operating frequencies (0.9 GHz, 1.8 GHz and 2.7 GHz)
with isolation resistor, R, and lumped elements L and C. The circuit is simulated for
configurations of various combinations of lumped elements (RL, RC and RLC).
From the simulation results obtained, the design cannot be archived therefore it has
been changed to single operating frequency. The simulation results for different
operating frequencies are shown in Appendix A.
By using single operating frequency, the desired response can be obtained
and can be improved. The design has proceeded with operating frequency at 0.9
GHz. The schematic circuit for the Tri Section Modified WPD is shown in Figure
4.11. The simulated results are given in Figures 4.12 to 4.14.
Figure 4.11
The schematic layout for basic Tri Section Modified WPD.
35
Figure 4.12
Figure 4.13
Simulated return loss of basic Tri Section Modified WPD.
Simulated isolation of basic Tri Section Modified WPD.
36
Figure 4.14
Simulated power division of basic Tri Section Modified WPD.
It can be seen that the Tri Section Modified WPD exhibits excellent return
losses of -120 dB at all ports, at the first 3 frequencies. The -10 dB BW for the input
is 0.6 GHz while for the output is 0.8 GHz, which are still narrowband. The circuit
also exhibits excellent isolation of -120 dB at 0.5 GHz, 1.5 GHz and 2.5 GHz
between ports 2 and 3 and vice-versa. It also exhibits equal power division from
Port 1 to Ports 2 and 3; at 0.5 GHz, 1.5 GHz and 2.5 GHz.
It can be inferred that some improvements have been obtained, however the
circuit is still narrowband. Hence, lumped elements of R, L and C have been
introduced to the circuit, as depicted in Figure 4.15. The simulation for this
configuration was done at 0.9 GHz. The results are shown in Figures 4.16 to 4.18.
37
(i)
Tri Section Modified WPD with RL Element
The configuration uses three sections of quarter-wave transformer with
resistor and inductor (R and L) as isolating components between the output ports.
The value of R is 100 Ω and value of L for this simulation is set as a variable for
further investigations. The results are tabulated in Table 4.3.
Figure 4.15
The schematic layout for Tri Section Modified WPD with RL
Element.
Figure 4.16
Simulated return loss of Tri Section Modified WPD with RL
Element.
38
Figure 4.17
Simulated isolation of Tri Section Modified WPD with RL Element.
Figure 4.18
Simulated coupling or power division of Tri Section Modified WPD
with RL Element.
39
Table 4.3
Simulated results with varying L.
Values of L
S11
S22
S23
1 nH
- 120 dB
- 7 dB
- 6 dB
10 nH
- 120 dB
- 9 dB
- 11 dB
100 nH
- 120 dB
- 25 dB
- 14 dB
1000 nH
-120 dB
- 46 dB
- 15 dB
It can be inferred that the circuit exhibits excellent input return loss
of -120 dB but at lower three frequencies. Reasonably good output return
losses at output ports were obtained, but at higher three frequencies.
Reasonably good isolation of less than -15dB between ports 2 and 3 and
vice-versa, at three higher frequencies were observed. However, equal
power division of -3 dB at output ports at the three lower frequencies were
achieved.
(ii)
Tri Section Modified WPD with RC Element
The configuration still uses Tri Section Modified WPD but with
changing values of the lumped elements R and C. The component R of 100
Ω and varying C were used. The schematic is shown in Figure 4.19, while
the simulated results are depicted in Figures
40
Figure 4.19
The schematic layout for Tri Section Modified WPD with RC
Element.
Figure 4.20
Simulated return loss of Tri Section Modified WPD with RC
Element.
41
Figure 4.21
Simulated isolation of Tri Section Modified WPD with RC Element.
Figure 4.22
Simulated coupling or power division of Tri Section Modified WPD
with RC Element.
42
Table 4.4
Simulated results with varying C.
Values of C
S11
S22
S23
1 pF
-105 dB
-23 dB
-41 dB
0.1 pF
-105 dB
-43 dB
-42 dB
0.01 pF
-106 dB
-62 dB
-83 dB
It can be inferred that the circuit exhibits excellent input return loss
of -105 dB but at lower three frequencies. Reasonably good output return
losses at output ports were obtained, but at higher three frequencies. The -10
dB BW is 0.6 GHz at the input and 0.85 GHz at the output. This is still
narrowband, however it is broader compared to the circuit with R and RL.
Excellent isolation of less than -41 dB between ports 2 and 3 and vice-versa,
at the lower three frequencies were observed. However, equal power
division of -3 dB at output ports at the three lower frequencies were
achieved.
(iii)
Tri Section Modified WPD with RLC Element
The configuration maintains Tri Section WPD but RLC loading is
varied. The value of R is set as 100 Ω and. L and C were fined-tuned for
optimum performance. The schematic layout is shown in Figure 4.23, while
the simulated results are presented in Figures 4.24 to 4.26.
43
Figure 4.23
The schematic layout for Tri Section Modified WPD with RLC
Element.
Figure 4.24
Simulated return loss of Tri Section Modified WPD with RLC
Element.
44
Figure 4.25
Simulated isolation of Tri Section Modified WPD with RLC
Element.
Figure 4.26
Simulated coupling or power division of Tri Section Modified WPD
with RLC Element.
45
Table 4.5
Simulated results with varying L and C.
Values of L & C
L
C
1 nH
1 pF
S11
S22
S23
-106 dB
-6 dB
-6 dB
10 nH
1 pF
-106 dB
-7 dB
-8 dB
100 nH
1 pF
-106 dB
-59 dB
-60 dB
1000 nH
1 pF
-106 dB
-23 dB
-40 dB
1000 nH
0.1 pF
-106 dB
-79 dB
-80 dB
1000 nH
0.01 pF
-106 dB
-42 dB
-42 dB
The configuration exhibits excellent return losses of -106 dB at the 3 lower
frequencies, at all ports, with RLC loading. The -10 dB BW broadens with 0.6 GHz
and 0.9 GHz at the input and output, respectively. However, the BW is till
narrowband. Excellent isolation of less then -40 dB was observed between ports 2
and 3, and vice-versa, at the lower 3 frequencies. This is with the exception for the
first two sets of RL. Greatest isolation at 1.4 GHz and have an equal power division
of -3 dB at output ports at the 3 frequencies with minute loss of 0.4 dB which is
acceptable. It can be inferred that an improvement has been obtained, through finetuning of the the L and C elements.
4.3
Tri Section Modified Wilkinson Power Divider with R Segment in
Cascade
Further modifications were done in terms of having different R segment in
cascade.
46
(i)
Tri Section Modified WPD with 2nd Segment in Cascade
Figure 4.27
The schematic layout for Tri Section Modified WPD with 2nd
Segment in Cascade.
Figure 4.28
Simulated return loss of Tri Section Modified WPD with 2nd
Segment in Cascade.
47
Figure 4.29
Simulated isolation of Tri Section Modified WPD with 2nd Segment
in Cascade.
Figure 4.30
Simulated power division of Tri Section Modified WPD with 2nd
Segment in Cascade.
48
From the simulated performed in Figure 4.28 to 4.30, S22 and S33 shown
excellent return losses less then -20 dB for output ports but behaviour at input
remains and narrows bandwidth. The optimum output return losses observed at 1.3
GHz with excellent isolation -50 dB. The equal power division of -3 dB at output
ports, at the 3 frequencies.
(ii)
Tri Section Modified WPD with at 1st Segment in Cascade
The schematic diagram is depicted in Figure 4.31. The simulated results are
given in Figures 4.32 to 4.34.
Figure 4.31
The schematic layout for Tri Section Modified WPD with 1 st
Segment in Cascade.
49
Figure 4.32
Simulated return loss of Tri Section Modified WPD with 1 st Segment
in Cascade.
Figure 4.33
Simulated isolation of Tri Section Modified WPD with 1st Segment
in Cascade.
50
Figure 4.34
Simulated power division of Tri Section Modified WPD with 1st
Segment in Cascade.
The configuration exhibits excellent return losses of less than -20 dB and the
behaviour of BW at the input remains narrowband. The optimum output return
losses were observed at 0.6 GHz and 2.2 GHz with excellent improved isolation
between ports 2 and 3, and vice versa with broader characteristic. The optimum
isolations are at 0.4 GHz and 2.3 GHz with equal power division of -3 dB at the
output ports, at the 3 frequencies.
51
(iii)
Tri Section Modified WPD with Full Segment in Cascade
Figure 4.35
The schematic layout for Tri Section Modified WPD with Full
Segment in Cascade.
Figure 4.36
Simulated return loss of Tri Section Modified WPD with Full
Segment in Cascade.
52
Figure 4.37
Simulated isolation of Tri Section Modified WPD with Full Segment
in Cascade.
Figure 4.38
Simulated power division of Tri Section Modified WPD with Full
Segment in Cascade.
53
The broadband feature is observed at the outputs ports up to 2.5 GHz. These
have been archived by modifying the segment through cascading and finetune the
values of RLC. However the modifications affect only the output ports. Therefore
tuning process has been made by tuning the impedance of transmission lines for the
final design circuit. The configuration exhibits excellent isolation between output
ports with broadband characteristic from 0.2 GHz to 2.5 GHz. Optimum isolations
are observed at 0.4 GHz and 2.2 GHz with equal power division of -3 dB at the
output ports.
4.4
Improving the Modified Wilkinson Power Divider
Final Modified WPD with full segment in cascade and modification of the
transmission line impedance were implemented. These modifications improved the
input and broadband characteristics of the return losses. By changing the operating
frequency from 0.9 GHz to 1 GHz, it has increased the bandwidth from 2.7 GHz to
3 GHz.
The schematic layout of the configuration is depicted in Figure 4.39. The
simulated performances are depicted in Figures 4.40 to 4.42. Excellent broadband
return losses over 3 GHz range have been achieved. The output ports are equally
better matched with the optimums occur at 1.5 GHz and the desired specifications
achieved. The improved configuration exhibit excellent isolation between the output
ports (from 0.2 GHz to 2.8 GHz). The equal power division of -3 dB has been
achieved between output ports.
54
Figure 4.39
The schematic layout for Final Design of Tri Section Modified WPD
with Full Segment in Cascade.
Figure 4.40
Simulated return loss for Final Design of Tri Section Modified WPD
with Full Segment in Cascade.
55
Figure 4.41
Simulated isolation for Final Design of Tri Section Modified WPD
with Full Segment in Cascade.
Figure 4.42
Simulated power division for Final Design of Tri Section Modified
WPD with Full Segment in Cascade.
56
4.5
Summary
It can be summarise that the proposed Modified WPD configuration with
full R loaded exhibit broadband characteristics, compared to the conventional WPD.
The performance comparisons between all WPD configurations are tabulated in
Table 4.6. It can be concluded that the modified WPD has improved the output
characteristics through the introduction of a 1st, 2nd and full segment in cascades.
The modified configuration has broadened the bandwidth characteristic through fine
tuning of the RLC elements. The bandwidth of the output ports broadened through
cascading of segment/s and the design allows flexibility of having an identical
output. The improved modified WPD has operating frequency of 1 GHz, being
improved from 0.9 GHz. This causes the BW to increase from 2.7 GHz to 3 GHz.
The improvement is achieved by tuning the impedance of the transmission line (Z1,
Z2 and Z3).
Table 4.6
Performance comparisons between all WPD configurations.
BW
Design Circuit
Optimum
Return
Isolation
Loss (S22 )
(S 23)
-120 dB
-120 dB
Basic Modified WPD
Input
(S 11)
0.6 GHz
Output
(S 22)
0.8 GHz
Modified WPD with RL
0.6 GHz
0.15 GHz
-18 dB
-15 dB
Modified WPD with RC
0.6 GHz
0.85 GHz
-50 dB
-70 dB
Modified WPD with RLC
0.6 GHz
0.9 GHz
-42 dB
-42 dB
Modified WPD with 2nd
Segment Cascade
0.9 GHz
2.7 GHz
-50 dB
-50 dB
Modified WPD with 1st
Segment Cascade
0.9 GHz
2.7 GHz
-45 dB
-30 dB
Modified WPD with Full
Segment Cascade
0.9 GHz
2.7 GHz
-25 dB
-40 dB
3 GHz
3 GHz
-28 dB
-38 dB
Improvement Modified
WPD (Final Design)
57
CHAPTER V
CONCLUSION AND RECOMMENDATIONS
5.1
Conclusions
The objective of the project is to design a broadband modified power divider
operating from 0.7 GHz to 3 GHz. It has the capability of delivering an identical
signal as the backup to a radar electronic warfare transceiving system. The work
involved MWO simulations.
The design starts with single stage WPDs operating at 0.9 GHz, 1.8 GHz and
2.7 GHz. It was found that the input and output return losses exhibit narrowband
operations. The investigation has identified to modify the configuration into
multistage circuit with three segments. Each segment operates at a different
operating frequency. However, the circuit did not perform as desired.
The design proceeded with single frequency segments of 0.9 GHz and RLC
load elements, segment cascading and tuning the impedance of transmission line.
The process has finally improved the -10 dB bandwidth into a broadband
characteristic with equal power division at all output ports. The configuration has
showed that it fulfills the desired specifications.
58
Through the integration of the circuit into the current ELINT system, it can
provide an extra output of equal power to the system. The signal can be used as
backup, for research activities, investigation purposes and etc. It can also provide
cost saving due to low maintenance cost. The capabilities of the system can be
improved without changing the original system.
5.2
Suggestions for Further Research
Suggestions for further research are as follows:
(a)
adapt the proposed design for other sections of the receiving ELINT
antenna (from 3 GHz to 10 GHz, and 10 GHz to 18 GHz).
(b)
design the combiner component for combining all the designed
sections of ELINT.
(c)
perform physical implementation and test to the real ELINT system.
59
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62
APPENDIX A
SIMULATION RESULTS FOR TRI SECTION MODIFIED WPD
All simulations were done using 3 different frequencies (0.9 GHz, 1,8 GHz and 2.7 GHz)
1.
Tri Section Modified WPD with RL Element (L = variable)
L = 1nH
L = 10nH
L = 100nH
L = 1000nH
63
2.
Tri Section Modified WPD with RC Element, (C = variable)
C = 1 pF
C = 0.1 pF
C = 0.01 pF
C = 0.001 pF
64
3.
Tri Section Modified WPD with LC Element, (L and C = variable)
L = 1000 nH & C = 0.001 pF
L = 100 nH & C = 0.01 pF
L = 10 nH & C 0.1 pF
L = 1 nH & 1 pF
65
4.
Tri Section Modified WPD with RLC Element, (L and C = variable)
L = 1 nH & 1 pF
L = 10 nH & 1 pF
L = 100 nH & 1 pF
L = 1000 nH & 1 pF
66
L = 1000 nH & 0.1 pF
L = 1000 nH & 0.01 pF
L = 1000 nH & 0.001 pF
L = 1000 nH & 0.0001 pF
67
5.
Tri Section Modified WPD with 2nd Segment Cascade, (R2 = variable)
R2 = 50
R2 = 100
R2 = 200
R2 = 300
68
6.
Tri Section Modified WPD with 2nd Segment Cascade, (Z1 = variable)
Z1 = 90
Z1 = 80
Z1 = 70
Z1 = 60
Z1 = 50
69
7.
Tri Section Modified WPD with 2nd Segment Cascade, (Z2 = variable)
Z2 = 90
Z2 = 80
Z2 = 70
Z2 = 60
Z2 = 50
70
8.
Tri Section Modified WPD with 2nd Segment Cascade, (Z3 = variable)
Z3 = 90
Z3 = 80
Z3 = 70
Z3 = 60
Z3 = 50
71
9.
Tri Section Modified WPD with 2nd Segment Cascade, (Z1 & Z3 =
variable)
Z1 = 90 & Z3 = 50
Z1 = 85 & Z3 = 55
Z1 80 = & Z3 = 60
Z1 = 75 & Z3 = 65
Z1 = 70 & Z3 = 70
Z1 = 65 & Z3 = 75
Z1 = 60 & Z3 = 85
Z1 = 55 & Z3 = 90
72
10.
Tri Section Modified WPD with 1st Segment Cascade, (R1 = variable)
R1 = 50
R1 = 100
R1 = 200
R1 = 300
73
11.
Tri Section Modified WPD with 1st Segment Cascade, (Z1 = variable)
Z1 = 90
Z1 = 80
Z1 = 70
Z1 = 60
Z1 = 50
74
12.
Tri Section Modified WPD with 1st Segment Cascade, (Z2 = variable)
Z2 = 90
Z2 = 80
Z2 = 70
Z2 = 60
Z2 = 50
75
13.
Tri Section Modified WPD with 1st Segment Cascade, (Z3 = variable)
Z3 = 90
Z3 = 80
Z3 = 70
Z3 = 60
Z3 = 50
76
14.
Tri Section Modified WPD with 1st Segment Cascade, (Z1 & Z3 =
variable)
Z1 = 90 & Z3 = 50
Z1 = 85 & Z3 = 55
Z1 = 80 & Z3 = 60
Z1 = 75 & Z3 = 65
Z1 = 70 & Z3 = 70
Z1 = 65 & Z3 = 75
Z1 = 60 & Z3 = 85
Z1 = 55 & Z3 = 90
77
15.
Tri Section Modified WPD with Full Segment Cascade, (R1 and R2 =
variable)
R1 = 50 & R2 = 50
R1 = 100 & R2 = 50
R1 = 200 & R2 = 50
R1 = 300 & R2 = 50
78
R1 = 300 & R2 = 100
R1 = 300 & R2 = 200
R1 = 300 & R2 = 300
79
16.
Tri Section Modified WPD with Full Segment Cascade, (Z1 = variable)
Z1 = 90
Z1 = 80
Z1 = 70
Z1 = 60
Z1 = 50
80
17.
Tri Section Modified WPD with Full Segment Cascade, (Z2 = variable)
Z2 = 90
Z2 = 80
Z2 = 70
Z2 = 60
Z2 = 50
81
18.
Tri Section Modified WPD with Full Segment Cascade, (Z3 = variable)
Z3 = 90
Z3 = 80
Z3 = 70
Z3 = 60
Z3 = 50
82
19.
Tri Section Modified WPD with Full Segment Cascade, (Z1 & Z3 =
variable)
Z1 = 90 & Z3 = 50
Z1 = 85 & Z3 = 55
Z1 = 80 & Z3 = 60
Z1 = 75 & Z3 = 65
Z1 = 70 & Z3 = 70
Z1 = 65 & Z3 = 75
Z1 = 60 & Z3 = 85
Z1 = 55 & Z3 = 90
83
20.
Tri Section Modified WPD with Full Segment Cascade, at fo, 2fo, 3fo
(fo = 1 GHz)
Z1 = 90 & Z3 = 50
Z1 = 85 & Z3 = 55
Z1 = 80 & Z3 = 60
Z1 = 75 & Z3 = 65
Z1 = 70 & Z3 = 70
Z1 = 65 & Z3 = 75
Z1 = 60 & Z3 = 80
Z1 = 55 & Z3 = 85